I have to wait for awhile then I am able to add more artists, but then receive the same error after adding ~5 artists. Is there something im doing wrong or is headphones quering musicbrainz for too much information?

Same thing here. First time I test the application.
Every artist it searches causes an entry like this in the log:
WARNING: Attempt to retrieve artist information from MusicBrainz failed for artistid: ... Sleeping 5 seconds
together with this one:
WARNING: Attempt to query MusicBrainz for ... failed: HTTP Error 403: Forbidden

What is strange is, I am able to query musicbrainz via the web service manually, eg pointing my browser to:http://www.musicbrainz.org/ws/2/artist/?query=artist:muse
turns up an xml result.
I assume it is this web API that is used, haven't had the time to have a look at the source yet.

It seems that MusicBrainz rejects those requests because of a not compliant user agent.

userAgent is defined in webservice.py (under headphones/lib/musicbrainz2).
After line 249 i added a new line which appends a URL to the user agent:
userAgent = 'python-musicbrainz/' + musicbrainz2.version
userAgent = userAgent + ' ( https://github.com/rembo10/headphones/ )'

Please see my comment on the pull request; there is an updated version of python-musicbrainz2 that can deal with setting a proper User-Agent without you needing to play around with custom patches to your libraries, which I'm sure you'd prefer to avoid :)